There are many sensory cues which contribute to the human ability to visually perceive depth and distance. Relative size, perspective, atmospheric effects, etc. all contribute, but the most important is stereoscopic vision. It is, in fact, the only visual cue by which we directly perceive depth, as opposed to distance.
Stereoscopic vision is the image perceived by the brain of the two subtly different views received by our two eyes, i.e. the parallax effect. By closing one eye and then the other, people can observe a relative motion of near objects against far objects. In fact the nearer the object the greater is its displacement in the visual field. This displacement is "computed" by the brain, leading to the perception of depth.
The parallax effect can be used advantageously in forming Random Dot Stereograms (RDS), flat images that have the appearance of three dimensions. These stereograms are a fascinating and entertaining diversion. In addition, the process of viewing stereograms may have a relaxing or even therapeutic effect on the human mind. There is limited anecdotal evidence that viewing RDSs may be useful in pain control therapy.
For example, Dual Image Random Dot Stereograms (DIRDS) were disclosed in an article by Professor Paul S. Boyer of Farleigh Dickinson University in Stereo World, March/April 1990, pp. 30-33. As noted in this article, the human brain has a remarkable ability to extract coherent images from otherwise random patterns, and this ability can be used to decode apparent three dimensional images from a DIRDS, constructed from a pattern of random dots in a pair of images.
To construct a DIRDS, one begins with two separate identical random dot pattern images (one for each eye) as shown in FIG. 1A. If one image is observed with one eye and one with the other, and the images are aligned properly, they will combine optically and appear as a flat plane with the original random pattern on it.
To create a depth effect, an area in one of the images, for example a circle, is marked off and all the dots inside this area are moved a very small distance to the side as shown in FIG. 1B. The random pattern of dots in the images masks the resulting difference from detection on casual comparison of the two images. However, if one eye is used to view each of the images, the brain will after some time "decode" the offset of the random dot pattern and process this detected offset as depth information. In the example of FIG. 1B where the shifted area is circular, the viewer will see a circle apparently "floating" in space over the random dot background. Multiple depths can be created by adjusting the distance of movement of the dot groups. In addition to the circle, FIG. 1B also has a square section of dots in the center area of the circle, which have been moved a distance greater than the distance moved by the dots defining the circle. In this way, a square is created which is apparently located at a higher level than the circle (i.e. floating above the circle).
This dual image technique has been implemented in the past using a computer that produces a random dot pattern in which each pixel is randomly selected to be a particular color (e.g. black or white).
It is also possible to create a Single Image Random Dot Stereogram (SIRDS), as disclosed in an article by Dan Dyckman in Stereo World, May/June 1990, pages 12-13. SIRDS are created using a technique which is slightly more subtle but relies upon the same general principle of parallax viewing as the DIRDS. A single image is divided into a number of columns of random dots, each column having a defined width in pixels (e.g. 50 to 200) which determines the "interocular distance" of the image. The first column on the left is purely random. The second one is a reproduction of the first, except that pixels in the selected area are adjusted to implant the hidden pattern shift which will be perceived by the human brain as depth information.
Next, a third column is put in copying the second column, except for selected pixels which, as before, are shifted a bit to the side. This process is repeated until the whole image is completed. Columns one and two form a pair, column two and three form a pair, columns three and four form a pair etc. all the way across the image.
By defining several areas of shift in an appropriate way, it is possible to create an illusion of many different perceived depths.
The viewing of SIRDS and DIRDS is a "skill" which requires that one learn a particular mode of focusing the eyes. Like riding a bicycle, viewing these images requires some practice at first; once viewing has been achieved, however, it is relatively easy for an individual to view a large variety of these images. As an aid to viewing, various techniques can be used with the "Dual Image" technique. One aid is a sheet of opaque material, such as cardboard, placed at right angles to the surface on which the dual images appear, aligned with the space between the images. One eye goes on each side of the cardboard, at the top, allowing each eye to see only one of the images. Another method uses two magnifying lenses (one for each eye) while holding the two images quite close to the eyes. The proximity forces the eyes to separate the images, while the lenses allow them to focus. The cardboard technique does not function with the SIRDS, since there are several pairs of dot groups hidden in a single image. However, magnifying lenses may be useful in viewing SIRDS.
A careful look at any of the objects depicted in three dimensions in a prior art SIRDS will reveal a distinct layering, as in a contour map. The techniques used in the prior art involve placing a specific dot in a specific dot location. That is, the random dots exist in a matrix whose cells are of a specific size. A given cell is either black or white. First, the random dots are created by random coloration of each cell in the matrix. Then, to create the image, selected areas of random dots are shifted by a distance which is a multiple of the matrix cell size. FIG. 2 is a magnified view of a portion of a SIRDS, showing the formation of a conventional random dot pattern.
Given modern printing technology, it would be possible in theory to make these dots very small. In the prior art, the dimension of a dot is used as a quantum of movement for groups of dots, and thus the dimension of a dot determines the apparent distance between possible altitudes in the three dimensional image. Based on this principle, smaller dots would seem to provide greater resolution in created apparent altitudes, and thus impart a high level of smoothing to the contours of three dimensional images in a RDS. For example, widely available laser printers can print at a resolution of 300 pixels per inch. Therefore, the inventors have experimented with the possibility of generating a SIRDS with the desired high resolution merely by reducing the size of the dots. However, the inventors have found that this technique does not produce acceptable results. For example, FIG. 2 is a SIRDS made with dots of reduced size. The image is therefore more detailed, and the contours are somewhat smoother than those in a SIRDS made with larger dots. However, as the dot size is further reduced beyond that shown, the ability of the eye to resolve the individual dots is also reduced. The finer dots look more like a uniform gray, and are very much more difficult to "see". Even at the limiting resolution of 300 DPI which is available on a laser printer, the results are useless for RDS production. The dots cannot be individually resolved by the human eye, and the viewer is thus unable to decode the depth information imprinted in the dot pattern. For this reason, the "dots" in prior art SIRDS are normally printed at a resolution on the order of 80 dots per inch or less, which did not permit high resolution in the perceived heights of the levels in the image, and therefore did not permit a smooth contour image.
As can be appreciated, there has necessarily been a tradeoff in the prior art between SIRDS with large dots and SIRDS with smaller dots. The larger dot SIRDS depict images looking like contour maps, but most people's ocular pattern recognition capabilities permit them to "see" these imprinted three-dimensional images. Smaller dots produce smoother images, but these images are undesirably harder to see, particularly for those with imperfect vision, and tend to appear as a uniform grayness as the dot size is reduced beyond the ability to resolve individual dots. The images made in the prior art with smaller dots may be so difficult to perceive that most people require aids such as magnifying lenses to compensate for the difficulty of resolving the small dot size.
Because of these problems, the prior art techniques of making RDSs were imperfect. The inventors believe that there is a need to form images with a smooth contour, while maintaining a dot size that permits better pattern recognition and resolution by the viewer. Far more pleasing and complex images would then be possible.